Problem: Khan.scratchpad.disable(); To move up to the maestro level in his piano school, William needs to master at least $107$ songs. William has already mastered $23$ songs. If William can master $8$ songs per month, what is the minimum number of months it will take him to move to the maestro level?
Answer: To solve this, let's set up an expression to show how many songs William will have mastered after each month. Number of songs mastered $=$ $ $ Months at school $\times$ Songs mastered per month $+$ Songs already mastered Since William Needs to have at least $107$ songs mastered to move to maestro level, we can set up an inequality to find the number of months needed. Number of songs mastered $\geq 107$ Months at school $\times$ Songs mastered per month $ +$ Songs already mastered $\geq 107$ We are solving for the months spent at school, so let the number of months be represented by the variable $x$ We can now plug in: $x \cdot 8 + 23 \geq 107$ $ x \cdot 8 \geq 107 - 23 $ $ x \cdot 8 \geq 84 $ $x \geq \dfrac{84}{8} \approx 10.50$ Since we only care about whole months that William has spent working, we round $10.50$ up to $11$ William must work for at least 11 months.